Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#35090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(12,13,15,17)(14,18,19,16)(23,30)(27,32)(29,34)(33,35);(12,14,15,19)(13,16,17,18)(21,25)(22,28)(27,32)(29,34);(8,9)(10,11)(12,13)(14,16)(15,17)(18,19)(20,21,24,25)(22,26,28,31)(23,27,30,32)(29,33,34,35);(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35);(20,23)(21,27)(22,29)(24,30)(25,32)(26,33)(28,34)(31,35)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 28078);